Author: Corinna Grobe
Topic: Modelling the exponential growth of the COVID19 cases in Switzerland.

Numerous reports focus on the development of case numbers over time. But hardly anyone talks about the growth and whether the measures we are taking in the fight against COVID19 are having an effect, in other words: are we beating the virus?

In mathematical epidemiology, time has no influence on the development of case numbers. In the SIR model, the three decisive variables are: Susceptible, Infected, Removed.

Therefore, in my presentation of the case numbers I will show new cases ~ Total confirmed cases. This is a better way to graph cases using a logarithmic scale in “phase space” - plotting the growth rate against the cumulative cases, rather than either of these against time. In this way it can be seen whether the growth is slowing down, i.e. whether the case numbers are no longer developing exponentially.

Inspiration for this presentation comes from this video by minutephysics (https://www.youtube.com/watch?v=54XLXg4fYsc) and the underlying dashboard build by Aatish Bhatia (https://github.com/aatishb/covid/blob/master/curvefit.ipynb).

Here’s Ben Spark explaining the SIR model in a wonderfully simple and understandable manner: https://www.youtube.com/watch?v=k6nLfCbAzgo

Variables:

Source: Bundesamt für Gesundheit (BAG), Daten des Situationsberichtes, Last retrieved: 31.03.2020


Loading libraries


library(readxl) # Version ‘1.3.0’
library(dplyr) # Version ‘0.8.4’
library(ggplot2) # Version ‘3.1.0’
library(statR) # Version ‘0.0.0.9000’
library(plotly)

Data import


Comment: COVID-19 case numbers since the introduction of mandatory reporting in Switzerland

## # A tibble: 6 x 2
##   Date                Cases
##   <dttm>              <dbl>
## 1 2020-02-24 00:00:00     3
## 2 2020-02-25 00:00:00     1
## 3 2020-02-26 00:00:00    14
## 4 2020-02-27 00:00:00    11
## 5 2020-02-28 00:00:00    10
## 6 2020-02-29 00:00:00    17

Calculating


Calculating change per day


## # A tibble: 6 x 5
##   Date                Cases Week    Daily_Total Daily_New
##   <dttm>              <dbl> <chr>         <dbl>     <dbl>
## 1 2020-02-24 00:00:00     3 2020-09           3         0
## 2 2020-02-25 00:00:00     1 2020-09           4         1
## 3 2020-02-26 00:00:00    14 2020-09          18        14
## 4 2020-02-27 00:00:00    11 2020-09          29        11
## 5 2020-02-28 00:00:00    10 2020-09          39        10
## 6 2020-02-29 00:00:00    17 2020-09          56        17

Calculating change per week


## # A tibble: 6 x 3
## # Groups:   Week [6]
##   Week    Weekly_Total Weekly_New
##   <chr>          <dbl>      <dbl>
## 1 2020-09            3         67
## 2 2020-10          102        368
## 3 2020-11          623       2173
## 4 2020-12         3612       6339
## 5 2020-13        10419       7190
## 6 2020-14        16176         36

Plotting the curve


Plotting Total Cases vs. New Cases for each day



Plotting Total Cases vs. New Cases for each week


Time is implied. Each point represents the calendar week starting with week 9 on the left and moving to week 14 on the right.

Week 14 currently ongoing. Weekly data not fully available yet.


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